Page:International Library of Technology, Volume 93.djvu/49

 The truth of these rules can easily be shown. Take formula 4, Art. 38, $pv⁄T$ = $p1v1⁄T1$ and assume that the temperature remains constant; that is, T$1$ = T. Then, $pv⁄T$ = $p1v1⁄T1$, or pv = p$1$v$1$. In the same way, let the pressure remain constant, so that p$1$ = p. Then, $pv⁄T$ = $pv1⁄T1$, or $v⁄T$ = $v1⁄T1$, or $v⁄v1$ = $T⁄T1$. Similarly, assuming the volume to remain constant, so that v$1$ = v$1$$pv⁄T$ = $p1v⁄T$, or $p⁄T$ = $p1⁄T1$, or $p⁄p1$ = $T⁄T1$.

In formulas 1, 2, and 3, it makes no difference in what units the pressures and, volumes are measured, except that they must be the same throughout an example, and the pressures must always be absolute pressures.

1. A vessel contains 25 cubic feet of gas at a pressure of 18 pounds per square inch; if 126 cubic feet of gas having the same pressure is forced into the vessel, what will be the resulting pressure? Ans. 108 lb. per sq. in.

2. A pound of air has a temperature of 126° F. and a pressure of 14.7 pounds; what volume does it occupy? Ans. 14.75 cu. ft.

3. A certain quantity of air has a volume of 26.7 cubic feet, a pressure of 19.3 pounds per square inch, and a temperature of 42° F.; what is the weight? Ans. 2.77 lb.

4. A receiver contains 180 cubic feet of gas at a pressure of 20 pounds per square inch; if a vessel holding 12 cubic feet is filled from the receiver until its pressure is 20 pounds per square inch, what will be the pressure in the receiver? Ans. 18$2⁄3$ lb. per sq. in.

5. Ten cubic feet of air having a pressure of 22 pounds per square inch and a temperature of 75° F. is heated until the temperature is 300° F.; the volume remaining the same, what is the new pressure? Ans. 31.25 lb. per sq. in.

41. Temperature, Pressure, and Volume of Gaseous Mixtures. — If two liquids that do not act chemically on each other are mixed together and allowed to stand, it will